where \(\texttt {BIN} \in \lbrace \texttt {BEFORE}, \texttt {EQUAL}, \texttt {MEETS}, ...\rbrace \) . In order to generalize the temporal relations from the data, one keeps track of the set of applicable temporal relations for each pair of the events in the rule. Whenever a positive query is matched by the rule, one updates the temporal relations to satisfy the time constraints posed in the corresponding subgraph of the query. This is the traditional path-consistency (PC) algorithm introduced in [1]}. In this work, we incorporate the PC algorithm and propose the modified PC for MRBW. The algorithm is shown Algorithm REF . Here, \(ResolveTime\)  is the standard PC algorithm. Intuitively, the modified PC algorithm resolves time constraints whenever the two random walk paths merges together. This way, one does not need to update the relations at each step of the random walk, because the events within each path is already ordered.
